It is known to polymerize a mixture of butenes in solution in a boiling liquid hydrocarbon polymerization medium, especially for manufacturing a liquid polybutene or polyisobutene. In general the solution polymerization is carried out continuously in a reactor with the aid of a catalyst of cationic type and optionally of a cocatalyst. A reaction instability has very frequently been observed in the polymerization reactor in such a process. This instability can be characterized especially by the manufacture of a polymer of a nonuniform quality, which has a molecular weight distribution which is too broad, generally with catalyst residues or chlorine residues in a quantity which is too large. It may also be characterized by difficulties in control of some polymerization parameters, such as the polymerization temperature, the mean residence time of the polymer in the reactor or the withdrawal of the polymer out of the reactor.